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As I understand it, it's the idea that there are no overarching, ubiquitous moral principles. Instead, all situations should be judged based on their own unique parts and nuances, and one can derive the moral action from each individual judgement.

Is that correct? If not, what philosophy is most similar to what I explained above?

Moral particularism comes in a few different flavours. The position you have mentioned seems to be at one extreme: We can totally deny that there are any abstract moral principles, and we shouldn't bother trying to reach for them.

For example, suppose the non-particularist claimed that pain always counted as a negative in all moral situations. The pain caused by the dentist is counted as bad, but it is overruled by the long-term good of the dentist. Here, the component of pain is small, but still a negative in the moral calculation. It would be morally better if the dentist didn't cause the pain, and morally worse if the dentist caused more pain that necessary.

From here, the non-particularist might be tempted to claim that pain always counts as a negative in all situations. From here there is hope for the non-particularist that components of different moral situations are always counted the same way, and that there is some stable pattern to be followed, and maybe even all-applicable moral principles.

The moral particularist denies this. They offer examples where pain counts as a good, such as in exercise or athletic competitions. There are cases where pleasure is counted as a bad, such as when a torturer gains pleasure from watching his victims suffer. The particularist wants to point out that pain can count as a moral positive in a final moral assessment. Similarly, pleasure can count as a negative. The particularist hopes to throw the whole project of abstract moral theorizing into doubt, since every small detail of every situation can change the moral value.

Jonathan Dancy is at this extreme of the particularist scale. See Margret Little and Mark Lance for a more moderate position on particularism.

For the moderate particularist, we can agree that there are these kind of abstract moral principles laying about, but they are defeasible and it is possible to override them if the situation is twisted enough. For example: Lying is wrong. Well usually, but not always. Lying about the cookies to your mother is wrong, but lying to the murderer to save the victim is justified. The moderate particularist likes to talk about 'standard' cases, which are ordinary situations where the moral rules always seem to work. But they also recognize 'deviant' cases where the moral rules get bent out of shape and are no longer appropriate.

Since the comment above beat me to the punch I would like to offer up a couple of philosophers so you can follow up.

The first is most similar to the definition given in the question. W.D. Ross has his paper "The Right and the Good". In this paper he agrees with Moore in saying that good is indefinable. Where he disagrees with Moore is in having a consequentialist ethics. Instead he opted for a light pluralism. He though that there were duties and the most important ones were he ones we could see Prima Facia.

The other is H.A. Pritchard. He has a paper called "Does Moral Philosophy rest on a mistake?" Ultimately yes it does. Trying to make the good the right is the mistake. He makes a stark separation between rightness a d goodness.